ACARA v9 CONTENT DESCRIPTION “connect objects to their nets and build objects from their nets using spatial and geometric reasoning”
Builds on Lines, Angles and Symmetry (AC9M4SP01). Year 4 explored three-dimensional objects and the flat shapes that make their faces; Year 5 connects the two directions, unfolding a solid into the flat net of its faces and folding a net back up into the solid it came from. Reasoning about which flat arrangement wraps into which object, and what each face, edge and corner becomes, is spatial thinking made concrete, and it underpins the volume, surface and design work of later years.
A solid unfolded is a net
A net is what you get when a three-dimensional object is unfolded and laid out flat, so that every face lies in one plane. Imagine cutting along some edges of a cardboard box and opening it out: the flat shape left on the table is a net of the box. Each face of the solid becomes one region of the net, joined to its neighbours along the edges that were not cut. A net is therefore not a new shape but the same solid seen flat, which is why thinking in nets links the flat geometry of faces to the solid geometry of objects.
A solid unfolded is a net
Unfold a cube and its faces lie flat as a net.
Six squares joined edge to edge are a net. Fold it to see the solid it makes.
The cube and its six squares
The cube is the clearest place to start, because all six of its faces are identical squares. Unfold a cube and you get six squares joined edge to edge, often in the shape of a cross, though several different arrangements fold up just as well. Counting the squares confirms the cube has six faces, and tracing which square meets which shows how the flat net wraps into a closed box. Folding a cube net in the mind, square by square, is the first real act of the spatial reasoning this unit is built on.
Read a net to predict its solid
The faces in a net tell you which solid it forms.
Which flat net folds into a cube?
Reading a net before it folds
The harder skill is to look at a flat net and see the solid it will become before any folding happens. The clues are the shapes of the faces and how many there are: six squares promise a cube, while one square joined to four triangles promises a square pyramid, and two triangles with three rectangles promise a triangular prism. Reading a net means matching the collection of flat faces to the object whose surface they form. This is reasoning, not memorising, because the same questions answer any net: what faces are here, how many, and how do they meet?
The cube and its six squares
The number of faces equals the number of pieces in the net.
How many faces does a cube have? Its net has one region per face.
Building the solid from its net
Folding works in the other direction, turning a flat net back into the solid it describes. As each face lifts and turns along its joins, flat regions that sat side by side rise to meet at edges, and the open shape closes into a solid. A child who can build the object from its net, in the hand or in the mind, has understood that the net carries all the information the solid needs: every face, in the right place, ready to fold. This back-and-forth between flat and solid is exactly the spatial and geometric reasoning the curriculum asks for.
Build the solid from its net
Name the solid a net of given faces will form.
A net of 6 squares folds into which solid?
Faces, edges and corners
Folding also explains the parts of a solid. Each flat region of the net becomes a face; the joins that the folds bring together become edges; and the points where edges meet become the corners, or vertices. So a cube net of six squares folds into a solid with six faces, twelve edges and eight vertices, and every one of them can be traced back to the flat net. Keeping track of what becomes a face, an edge or a corner stops the parts of a solid from blurring together and makes folding a careful, checkable act.
Faces, edges and corners
Each face of the solid is one region of its net.
Each solid unfolds into a net with one region per face. Reveal how many each one has.
From net to solid and back
Nets let us travel freely between flat and solid in both directions: unfold any object to read its faces, or fold any net to build its object. Six squares give a cube, a square with four triangles gives a square pyramid, and triangles with rectangles give a prism, each net carrying its solid's full surface. Moving between the two, and naming what each face, edge and corner becomes, is spatial reasoning a child can rely on, and it is the foundation for the volume, surface area and design problems that the rest of the geometry curriculum will bring.
Quick self-check
1. A net is...
2. How many square faces does a cube have?
3. A net of one square and four triangles folds into a...
4. A triangular prism's net is made of...
5. When a net is folded, each flat piece becomes a...